The only reason measures to curb disinformation would have a partisan impact is because conservative parties (throughout the industrialized world, not just in the US) use disinformation strategies far, far more than do other parties.
Center-left/left parties use reality to galvanize their base voters into action. Their voters are people who aren't pleased with what's happening in their countries and want to change it for the better. There's no need for center-left parties to lie that their electoral opponents eat babies when their electoral opponents actually put children in cages.
In contrast, right wing parties overcome the inherent unpopularity of their revealed policy platforms (running on platforms of cutting taxes on the very rich while making life harder for the average person is not popular) by using disinformation to make a stated platform based on fabricated wedge issues. Hence, the imaginary convoys of South American migrants that were about to storm the US-Mexico border in 2018.
As such, restricting disinformation will have a partisan impact. Within the US, there is no Democratic equivalent to Qanon, so anti-disinformation measures that impact the likes of Qanon will have no impact on the Democratic party whatsoever. This, however, isn't a bad thing.
Functioning societies can have zero tolerance for 'alternative facts.' Disagree over goals and interpretations, but facts must be accepted by all. Democracy requires an informed electorate and there can be no functioning democracy when one side is free to invent its own version of reality.